I got this trinket last night and the fun and testing ensued. Here are my findings. Some of you may not understand why I took this trinket, but if you look at the newly revised BiS 3.3 list for rets on EJ, you'll see.
Last night I ran ~2 hours worth of testing on target dummies with this trinket. I also brought along a rogue from the guild and let him use it prior to the trinket becoming bound to me.
As others have said, TAJ requires you to be standing right on top of the target of the proc (less than 2 yds). While running tests, I found that many of our abilities can proc a mote. Judgement, DS, CS, auto, and seal damage can all grant a mote.
For AoE testing, I switched from single targeting the boss dummy to attacking the lvl 60 dummies with DS/SoComm. I found that a single DS with SoComm active can provide many motes in one single attack. With a 4stack of motes and hitting DS, I watched as my stack dropped after hitting 8 motes, then rebuilt back up to 2. Many times I saw single DS/SoComm attacks provide anywhere from 3-6 motes while standing in the middle of the 4 lvl 60 dummies.
The proc: It seems that the proc is directed at the target that granted you the 8th mote. While attacking those lowbie aoe dummies, I found that I was not getting the proc once I hit an 8 stack. The stack would reset and no damage proc went off regardless of how close I was standing to my primary target. In this case with 4 targets, you only proc the damage every ~3 stacks because it will likely gain the 8th mote from one of your splash damage targets.
I made one other observation that I found to be pretty cool. When auto-attacking the boss level dummy with Seal of Corruption active, I watched as the TAJ procs actually added Seal of Corruption damage. I could have expected this after hearing that the TAJ proc can also proc poisons for rogues.
The proc damage obviously varies based on your gear. For my tests, the proc damage was 1300-1700 non-crit and 2500-3700 crit. I ran numerous tests and didn't take any screens of them. Because so many abilities can proc a mote, my recount log showed the number of anger procs was very high in comparison to my melee attacks. Going all out with all damage attacks for a total of 200 melee attacks, I gained 119 damage procs from this trinket. So many different attacks contribute to this proc that it is dealing damage on basically every other auto-attack.
In single target testing, the proc comprised of 3.4% of my total damage. For my mutilate rogue guildmate, the proc was 1.3% of his damage. This doesn't factor in the bonus seal damage delivered from the proc or the poison procs for the rogue. His proc damage was 300-400 non-crit and 700-800 crit.
For clarification when i referenced the proc, I was referring to the damage dealing aspect of this trinket. For this post proc=/=gaining a mote.